How do I convert an inertia tensor from body space to world space?

[ScanCrowRadio]

I've been trying to solve the following problem involving Angular Acceleration and the inertial tensor for about 2 weeks now. I know it's bad ask for a question to be solved, but I'm really at a loss here folks. I'm a high school student who has taken a physics class.

What I'm Trying To Do: I'm trying to give a 3D rigid body an angular acceleration α by applying a torque τ. This is for a program I am writing, so I need to calculate this every time the game updates. I'm working with the Navidia Physx API.

Question: How do I properly convert the inertial tensor, I, from body space to global space?

Starting Variables: desired angular acceleration α(angle axis representation) in global space, the inertia tensor of the object I in body space

What I am trying to find: The torque τ(angle axis representation) in global space that when applied to the body will give it the angular acceleration α.




I've already tried [I_g]=[R]^T[I_b][R] where [R] is the rotation matrix for the rigid body in question, I_g is the inertia tensor in global space, and I_b is the inertia tensor in body space. After I find this I_g , I convert α into Euler Angle representation and multiply it against I_g:
α_x * I_{g xx}
α_y * I_{g yy}
α_z * I_{g zz}

I also have tried keeping I in body space, converting α to body space and using I_m=n^T[I_b]n , where n is the axis of the axis angle representation of α, and I_m is the scalar moment of inertia about that axis. I then take this I_m and multiply it by α in global space.

Both of these calculations have ended up in error. If you would like me to post the code of both of these attempts I am willing to do so, just ask me in the comments.

If you covert between representations ( for example quaternion -> Euler angle), just mention it.

Even though this question is not from Home Work, if you think I should move this question over to HOMEWORK, just comment and I'll do so.

Thank you so much!

 

[eljose79]

I understand your struggle with trying to convert the inertia tensor from body space to global space. This can be a complex problem, especially for someone who has taken only a high school physics class.

Firstly, I want to clarify that the equation you have tried, [Ig]=[R]T[Ib][R], is correct. However, there may be some errors in your implementation of this equation. I recommend checking your code and making sure that you are using the correct rotation matrix and that you are properly multiplying the matrices.

In addition, I recommend double checking your conversion of α from Euler angle representation to axis-angle representation. Make sure that you are using the correct conversion equations and that you are applying them in the correct order.

Another thing to consider is the units of your inputs and outputs. Make sure that all of your values are in the correct units (e.g. radians for angles) and that your outputs are also in the correct units.

If you are still having trouble, it may be helpful to break down the problem into smaller steps and test each step individually. For example, first try converting α from Euler angle representation to axis-angle representation and then apply the rotation matrix to the inertia tensor. This can help you identify where the error is occurring.

Finally, I recommend checking the documentation for the Navidia Physx API to see if there are any specific guidelines or functions for converting the inertia tensor from body space to global space.

I hope this helps and good luck with your program! If you continue to have trouble, don't hesitate to reach out for further assistance.